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A210325
Number of 4-divided words of length n over a 3-letter alphabet.
3
0, 0, 0, 0, 6, 56, 343, 1534, 6067, 22162, 76899, 257792, 843616, 2712241, 8606426, 27040628, 84311895
OFFSET
1,5
COMMENTS
See A210109 for further information.
Row sums of the following table which shows how many words of length n over a 3-letter alphabet are 4-divided in k different ways:
6;
34, 13, 9;
159, 75, 51, 20, 13, 17, 5, 3;
500, 287, 266, 130, 71, 103, 37, 35, 33, 22, 15, 14, 13, 2, 3, 1, 2;
- R. J. Mathar, Mar 25 2012
REFERENCES
Computed by David Scambler, Mar 19 2012
PROG
(Python)
from itertools import product, combinations, permutations
def is4div(b):
for i, j, k in combinations(range(1, len(b)), 3):
divisions = [b[:i], b[i:j], b[j:k], b[k:]]
all_greater = True
for p, bp in enumerate(permutations(divisions)):
if p == 0: continue
if b >= "".join(bp): all_greater = False; break
if all_greater: return True
return False
def a(n): return sum(is4div("".join(b)) for b in product("012", repeat=n))
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Aug 28 2021
CROSSREFS
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Mar 20 2012
EXTENSIONS
a(14)-a(17) from Michael S. Branicky, Aug 28 2021
STATUS
approved